Statistics and Probability Answers

A random sample of size 144 is drawn from a population whose distribution, mean, and standard deviation are all unknown. The summary statistics are 𝑥̅= 58.2 and s = 2.6.

a. Construct an 80% confidence interval for the population mean μ.

b. Construct a 90% confidence interval for the population mean μ.

A random sample is drawn from a population of known standard deviation 11.3.

Construct a 90% confidence interval for the population mean based on the information

given (not all of the information given need be used).

a. n = 36, 𝑥̅= 105.2, 𝑠 = 11.2

b. n = 100, 𝑥̅= 105.2, 𝑠 = 11.2

Compute the population proportion interval estimate given n, p, and the confidence level

a. Confidence Level= 99%, p=0.4, n=40

b. Confidence Level= 90%, p=0.15, n=55

A question in Probability & Statics:-

At a checkout counter, customers arrive at an average of 1.5

per minute. Assuming poisson distribution

1- The probability of no arrival in two minutes is.....

2- The variance of the number of arrivals in two minutes

is.....

3- Suppose X has binomial distribution with n=1000 and p

=0.002 , Then P(x=3)=....

A secretary makes 2 errors per page on the average. What is the probability that on the next 

page she makes; 4 or more errors and no error?

Let X be a random variable with probability distribution

X -1 0 1 2 3

F(X) 0.125 .50 0.20 0.05 0.125

a) Find E(X) and VAR(X).

b) Find the probability distribution of the random variable Y= 2X+1. Using the 

probability distribution of Y determine E(Y) and VAR(Y).

A population consists of the values (1, 3, 4). From the list below, choose 9 possible samples of size 2 that can be drawn from this population with replacement

A sample of 390 senior high school students applied to different state universities, wherein 117 are female. Find the 99% confidence interval of the true population proportion who applies for different state universities

A school principal claims that grade 11 students have a mean grade of 86 with a standard deviation of 4. suppose that the distribution is approximately normal. What is the probability that a random selected grade will be less than 84?

Based on a study, the average typing speed of women is normally distributed. Karen verified the results by conducting a similar study and found out that the standard error of the sample mean is 9 words per minute using a sample with a variance of 1 215. Determine the variance of the sampling distribution